Turbine rotor blade airfoil profile

ABSTRACT

The present application provides a turbine rotor blade including an airfoil shape. The airfoil shape may have a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I. The Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances expressed in a unit of distance (e.g., inches) by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in the unit of distance. The X and Y values, when connected by smooth continuing arcs, define airfoil profile sections at each Z value. The airfoil profile sections at Z values may be joined smoothly with one another to form a complete airfoil shape.

FIELD

The present disclosure relates to an airfoil for a turbine rotor bladeof a stage of a turbine and, more particularly, relates to a shapedefining a profile for an airfoil of a turbine rotor blade.

BACKGROUND

Some jet aircraft and simple cycle or combined cycle power plant systemsemploy turbines, or so-called turbomachines, in their design andoperation. Some of these turbines employ airfoils (e.g., stator vanes ornozzles and rotor blades), which during operation are exposed to fluidflows. These airfoils are configured to aerodynamically interact withthe fluid flows and to generate energy from these fluid flows as part ofpower generation. For example, the airfoils may be used to createthrust, to convert kinetic energy to mechanical energy, and/or toconvert thermal energy to mechanical energy. As a result of thisinteraction and conversion, the aerodynamic characteristics of theseairfoils may result in losses that have an impact on system and turbineoperation, performance, thrust, efficiency, and power.

BRIEF DESCRIPTION

Aspects and advantages of the turbines and turbine rotor blades inaccordance with the present disclosure will be set forth in part in thefollowing description, or may be obvious from the description, or may belearned through practice of the technology.

In accordance with one embodiment, the present application provides aturbine rotor blade including an airfoil shape. The airfoil shape mayhave a nominal profile substantially in accordance with Cartesiancoordinate values of X, Y and Z set forth in Table I. The Cartesiancoordinate values of X, Y and Z are non-dimensional values from 0% to100% convertible to dimensional distances expressed in a unit ofdistance by multiplying the Cartesian coordinate values of X, Y and Z bya height of the airfoil in the unit of distance (e.g., inches). The Xand Y values, when connected by smooth continuing arcs, define airfoilprofile sections at each Z value. The airfoil profile sections at Zvalues may be joined smoothly with one another to form a completeairfoil shape.

In accordance with another embodiment, the present application providesa turbine rotor blade including an airfoil having an uncoated nominalsuction-side profile substantially in accordance with suction-sideCartesian coordinate values of X, Y and Z set forth in Table I. TheCartesian coordinate values of X, Y and Z are non-dimensional valuesfrom 0% to 100% convertible to dimensional distances expressed in a unitof distance by multiplying the Cartesian coordinate values of X, Y and Zby a height of the airfoil in the unit of distance (e.g., inches). The Xand Y values, when connected by smooth continuing arcs, definesuction-side profile sections at each Z value. The suction-side profilesections at the Z values may be joined smoothly with one another to forma complete (uncoated) suction-side nominal shape of the airfoil.

In accordance with another embodiment, the present application providesa turbine with a plurality of turbine rotor blades, each having anairfoil having an airfoil shape. The airfoils each have a nominalprofile substantially in accordance with Cartesian coordinate values ofX, Y and Z set forth in Table I. The Cartesian coordinate values of X, Yand Z are non-dimensional values from 0% to 100% convertible todimensional distances expressed in a unit of distance by multiplying theCartesian coordinate values of X, Y and Z by a height of the airfoil inthe unit of distance. The X and Y values, when connected by smoothcontinuing arcs, define airfoil profile sections at each Z value. Theairfoil profile sections at the Z values may be joined smoothly with oneanother to form a complete airfoil shape.

These and other features, aspects and advantages of the present turbinesand turbine rotor blades will become better understood with reference tothe following description and appended claims. The accompanyingdrawings, which are incorporated in and constitute a part of thisspecification, illustrate embodiments of the technology and, togetherwith the description, serve to explain the principles of the technology.

BRIEF DESCRIPTION OF THE DRAWINGS

A full and enabling disclosure of the present turbines and turbine rotorblades, including the best mode of making and using the present systemsand methods, directed to one of ordinary skill in the art, is set forthin the specification, which makes reference to the appended figures, inwhich:

FIG. 1 is a schematic representation of an exemplary turbine havingmultiple stages with each stage including alternating rows of turbinerotor blades and stationary vanes or nozzles, according to at least oneembodiment of the present disclosure;

FIG. 2 is a perspective view of a turbine rotor blade, according to atleast one embodiment of the present disclosure; and

FIG. 3 provides a cross-sectional view of an airfoil portion of theturbine rotor blade of FIG. 2.

DETAILED DESCRIPTION

Reference now will be made in detail to embodiments of the presentturbines and turbine nozzles, one or more examples of which areillustrated in the drawings. Each example is provided by way ofexplanation, rather than limitation of, the technology. In fact, it willbe apparent to those skilled in the art that various modifications andvariations can be made in the present technology without departing fromthe scope or spirit of the claimed technology. For instance, featuresillustrated or described as part of one embodiment can be used withanother embodiment to yield a still further embodiment. Thus, it isintended that the present disclosure covers such modifications andvariations as come within the scope of the appended claims and theirequivalents.

The detailed description uses numerical and letter designations to referto features in the drawings. Like or similar designations in thedrawings and description have been used to refer to like or similarparts of the invention. As used herein, the terms “first”, “second”, and“third” may be used interchangeably to distinguish one component fromanother and are not intended to signify location or importance of theindividual components.

As used herein, the terms “upstream” (or “forward”) and “downstream” (or“aft”) refer to the relative direction with respect to fluid flow in afluid pathway. For example, “upstream” refers to the direction fromwhich the fluid flows, and “downstream” refers to the direction to whichthe fluid flows.

It is sometimes necessary to describe parts that are disposed atdiffering radial positions with regard to a center axis. The term“radially” refers to the relative direction (i.e., movement or position)that is substantially perpendicular to an axial centerline of aparticular component; the term “axially” refers to the relativedirection (i.e., movement or position) that is substantially paralleland/or coaxially aligned to an axial centerline of a particularcomponent; and the term “circumferentially” refers to the relativedirection (i.e., movement or position) that extends around the axialcenterline of a particular component.

Unless stated otherwise, terms of approximation, such as “generally,” or“about” include values within ten percent greater or less than thestated value. When used in the context of an angle or direction, suchterms include within ten degrees greater or less than the stated angleor direction. For example, “generally vertical” includes directionswithin ten degrees of vertical in any direction, e.g., clockwise orcounter-clockwise.

Referring now to the drawings, particularly to FIG. 1, an exemplaryturbine 10 of a gas turbine 12 includes a plurality of turbine stagesarranged in serial flow order. Each stage of the turbine includes a rowof stationary turbine nozzles or vanes (e.g., nozzles 100) disposedaxially adjacent to a corresponding rotating row of turbine rotor blades50. Four stages are illustrated in FIG. 1. The exact number of stages ofthe turbine 10 is a choice of engineering design and may be more or lessthan the four stages illustrated in FIG. 1. The four stages are merelyexemplary of one turbine design and are not intended to limit thepresently claimed turbine rotor blade in any manner.

The first stage comprises a plurality of turbine nozzles or vanes 100and a plurality of turbine rotor blades 150. The turbine nozzles 100 aremounted to a casing 16 of the turbine 12 and are annularly arrangedabout an axis of a turbine rotor 14. The turbine rotor blades 150 areannularly arranged about and coupled to the turbine rotor 14. A secondstage of the turbine 12 includes a plurality of turbine nozzles 200annularly arranged about the axis of the turbine rotor 14 and aplurality of turbine rotor blades 250 annularly arranged about andcoupled to the turbine rotor 14. The turbine nozzles 200 may be coupledto the casing 16 of the turbine 12.

As shown in FIG. 1, a third stage of the turbine 12 includes a pluralityof turbine nozzles 300 annularly arranged about the axis of the turbinerotor 14 and a plurality of turbine rotor blades 350 annularly arrangedabout and coupled to the turbine rotor 14. The turbine nozzles 300 maybe coupled to the casing 16 of the turbine 12. In particularembodiments, the turbine 12 includes a fourth stage which includes aplurality of turbine nozzles 400 annularly arranged about the axis ofthe turbine rotor 14 and a plurality of turbine rotor blades 450annularly arranged about and coupled to the turbine rotor 14. The fourthstage turbine nozzles 400 may be coupled to the casing 16 of the turbine12.

It will be appreciated that the turbine nozzles 100, 200, 300 and 400and turbine rotor blades 150, 250, 350 and 450 are disposed or at leastpartially disposed within a hot gas path 18 of the turbine 12. Thevarious stages of the turbine 10 at least partially define the hot gaspath 18 through which combustion gases, as indicated by arrows 20, flowduring operation of the gas turbine 12.

FIG. 2 provides a perspective view of an exemplary turbine rotor blade50 as may be incorporated in any stage of the turbine 12. For example,in one embodiment the turbine rotor blade 50 as presented in Table Ibelow is representative of a turbine rotor blade 350 of the plurality ofturbine rotor blades 350 of the third stage.

As shown in FIGS. 2 and 3 collectively, the turbine rotor blade 50includes an airfoil 52 having a pressure-side wall 54 and an opposingsuction-side wall 56. The pressure-side wall 54 and the suction-sidewall 56 meet or intersect at a leading edge 58 and a trailing edge 60 ofthe airfoil 52. A chord line 62 extends between the leading edge 58 andthe trailing edge 60 such that pressure and suction-side walls 54, 56can be said to extend in chord or chordwise between the leading edge 58and the trailing edge 60.

As shown in FIG. 2, the airfoil 52 includes a root or first end 64,which intersects with and extends radially outwardly from a base orplatform 66 of the turbine rotor blade 50. The airfoil 52 terminatesradially at a second end or radial tip 68 of the airfoil 52. Thepressure-side and suction-side walls 54, 56 can be said to extend inspan or in a span-wise direction 70 between the root 64 and/or theplatform 66 and the radial tip 68 of the airfoil 52. In other words,each turbine rotor blade 50 includes an airfoil 52 having opposingpressure-side and suction-side walls 54, 56 that extend in chord orchordwise 62 between opposing leading and trailing edges 58, 60 and thatextend in span or span-wise 70 between the root 64 and the radial tip 68of the airfoil 52.

In particular configurations, the airfoil 52 may include a fillet 72formed between the platform 66 and the airfoil 52 proximate to the root64. The fillet 72 can include a weld or braze fillet, which can beformed via conventional MIG welding, TIG welding, brazing, etc., and caninclude a profile that can reduce fluid dynamic losses as a result ofthe presence of fillet 72. In particular embodiments, the platform 66,the airfoil 52 and the fillet 72 can be formed as a single component,such as by casting and/or machining and/or 3D printing and/or any othersuitable technique now known or later developed and/or discovered. Inparticular configurations, the turbine rotor blade 50 includes amounting portion 74 (such as a dovetail joint), which is formed toconnect and/or to secure the turbine rotor blade 50 to the rotor shaft14.

The airfoil 52 of the turbine rotor blade 50 has a nominal profile atany cross-section taken between the platform 66 or the root 64 and theradial tip 68. A “profile” is the range of variation between measuredpoints on an airfoil surface and the ideal position listed in Table I.The actual profile on a manufactured turbine blade will be differentfrom those in Table I (e.g., due to coatings), and the design is robustto this variation, meaning that mechanical and aerodynamic function arenot impaired.

The X, Y, and Z values are given in Table I as percentage values of theairfoil height or span. As one example only, the height or radial spanof the airfoil 52 of turbine rotor blade 50 may be from about 10 inchesto about 20 inches (about 25 centimeters to about 51 centimeters).However, it is to be understood that heights below or above this rangemay also be employed as desired in the specific application.

A gas turbine hot gas path requires airfoils that meet systemrequirements of aerodynamic and mechanical blade loading and efficiency.To define the airfoil shape of each turbine rotor blade airfoil, thereis a unique set or loci of points in space that meet the stagerequirements and that can be manufactured. This unique loci of pointsmeet the requirements for stage efficiency and are arrived at byiteration between aerodynamic and mechanical loadings enabling theturbine to run in an efficient, safe and smooth manner. These points areunique and specific to the system.

The loci that define the turbine rotor blade airfoil profile include aset of about 2,400 points with X, Y and Z dimensions relative to areference origin coordinate system. The Cartesian coordinate system ofX, Y and Z values given in Table I below defines the profile of theturbine rotor blade airfoil at various locations along its height.

Table I lists data for an uncoated airfoil at cold or room temperature.The envelope/tolerance for the coordinates is about +1−5% in a directionnormal to any airfoil surface location and/or about +/−5% of the chord62 in a direction nominal to any airfoil surface location. In otherwords, the airfoil layout, as embodied by the disclosure, is robust tothis range of variation without impairment of mechanical and aerodynamicfunctions.

A point data origin 76 is defined at or proximate to the root 64 at theleading edge 58. In one embodiment as presented in Table I below, thepoint data origin 76 is defined at or proximate to (above or below) atransition or intersection line 78 defined between the fillet 72 and theairfoil 52. The point data origin 76 corresponds to the non-dimensionalZ value of Table I (presented below) at Z equals 0.

The coordinate values for the X, Y and Z coordinates are set forth innon-dimensionalized units provided in Table I, although other units ofdimensions may be used when the values are appropriately converted. TheX, Y and Z values set forth in Table I are also expressed innon-dimensional form (X, Y, and Z) from 0% to 100% of the height or spanof the airfoil 52. As one example only, the Cartesian coordinate valuesof X. Y and Z may be convertible to dimensional distances by multiplyingthe X, Y and Z values by a height of the airfoil at the leading edge 58and multiplying by a constant number (e.g., 100). As one example only,the Cartesian coordinate values of X, Y and Z may be convertible todimensional distances by multiplying the X, Y and Z values by a heightof the airfoil at the trailing edge 60 and multiplying by a constantnumber (e.g., 100).

To convert the Z value to a Z coordinate value, e.g., in inches, thenon-dimensional Z value given in Table I is multiplied by the Z heightof the airfoil in inches. As described above, the Cartesian coordinatesystem has orthogonally-related X, Y and Z axes and the X axis liesgenerally parallel to a centerline of the rotor shaft 14, i.e., therotary axis and a positive X coordinate value is axial toward an aft,i.e., exhaust end of the turbine 10. The positive Y coordinate valueextends tangentially in the direction of rotation of the rotor and thepositive Z coordinate value is radially outwardly from the base 66toward the radial tip 68. All the values in Table I are given at roomtemperature and do not include the fillet 72 or coatings (not shown).

By defining X and Y coordinate values at selected locations in a Zdirection normal to the X, Y plane, the profile section or airfoil shapeof the airfoil 52 of the turbine rotor blade 50, at each Z distancealong the length of the airfoil 52 can be ascertained. By connecting theX and Y values with smooth continuing arcs, each profile section at eachdistance Z is fixed. The airfoil profiles of the various surfacelocations between the distances Z are determined by smoothly connectingthe adjacent profile sections to one another to form the airfoilprofile.

The Table I values are generated and shown to four decimal places fordetermining the profile of the airfoil 52. As the turbine rotor blade 50heats up during operation of the gas turbine 12, surface stress andtemperature will cause a change in the X, Y and Z values. Accordingly,the values for the profile given in Table I define the “nominal” airfoilprofile, that is, the profile of an uncoated airfoil at ambient,non-operating or non-hot conditions (e.g., room temperature).

There are typical manufacturing tolerances as well as coatings whichmust be accounted for in the actual profile of the airfoil 52. Eachcross-section is joined smoothly with the other cross-sections to formthe complete airfoil shape. It will therefore be appreciated that +/−typical manufacturing tolerances, i.e., +/− values, including anycoating thicknesses, are additive to the X and Y values given in Table Ibelow. Accordingly, a distance of +/−5% in a direction normal to anysurface location along the airfoil profile defines an airfoil profileenvelope for this particular turbine rotor blade 50 airfoil design andturbine 12, i.e., a range of variation between measured points on theactual airfoil surface at nominal cold or room temperature and the idealposition of those points as given in Table I below at the sametemperature. The data provided in Table I is scalable (i.e., by uniformgeometric scaling), and the geometry pertains to all aerodynamic scales,at above and/or below 3000 RPM. The design of the airfoil 52 for turbinerotor blade 50 is robust to this range of variation without impairmentof mechanical and aerodynamic functions.

TABLE I SUCTION-SIDE PRESSURE-SIDE X (%) Y (%) Z (%) X (%) Y (%) Z (%)0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0157 0.4897 0.0000 0.2304−0.3670 0.0000 0.2669 0.9189 0.0000 0.6105 −0.5797 0.0000 0.5986 1.29030.0000 1.0285 −0.7043 0.0000 0.9693 1.6239 0.0000 1.4584 −0.7786 0.00001.3639 1.9279 0.0000 1.8889 −0.8176 0.0000 1.7756 2.2093 0.0000 2.321.3−0.8315 0.0000 2.1992 2.4717 0.0000 2.7537 −0.8239 0.0000 2.6335 2.71720.0000 3.1874 −0.7981 0.0000 3.0753 2.9482 0.0000 3.6210 −0.7578 0.00003.5241 3.1653 0.0000 4.0541 −0.7112 0.0000 3.9785 3.3699 0.0000 4.4877−0.6640 0.0000 4.4368 3.5650 0.0000 4.9208 −0.6187 0.0000 4.9006 3.75450.0000 5.3545 −0.5759 0.0000 5.3670 3.9383 0.0000 5.7881 −0.5363 0.00005.8353 4.1170 0.0000 6.2218 −0.4979 0.0000 6.3055 4.2901 0.0000 6.6555−0.4626 0.0000 6.7776 4.4575 0.0000 7.0898 −0.4293 0.0000 7.2522 4.61870.0000 7.5241 −0.3984 0.0000 7.7286 4.7741 0.0000 7.9584 −0.3707 0.00008.2063 4.9227 0.0000 8.3927 −0.3449 0.0000 8.6866 5.0649 0.0000 8.8276−0.3223 0.0000 9.1687 5.2002 0.0000 9.2619 −0.3021 0.0000 9.6528 5.32870.0000 9.6968 −0.2845 0.0000 10.1387 5.4495 0.0000 10.1324 −0.27000.0000 10.6258 5.5634 0.0000 10.5673 −0.2581 0.0000 11.1155 5.66850.0000 11.0029 −0.2499 0.0000 11.6058 5.7661 0.0000 11.4384 −0.24420.0000 12.0987 5.8555 0.0000 11.8740 −0.2411 0.0000 12.5921 5.93600.0000 12.3102 −0.2417 0.0000 13.0869 6.0072 0.0000 12.7463 −0.24610.0000 13.5828 6.0688 0.0000 13.1825 −0.2530 0.0000 14.0788 6.12170.0000 13.6181 −0.2637 0.0000 14.5754 6.1639 0.0000 14.0530 −0.27760.0000 15.0720 6.1966 0.0000 14.4873 −0.2952 0.0000 15.5686 6.21860.0000 14.9210 −0.3160 0.0000 16.0653 6.2300 0.0000 15.3540 −0.34110.0000 16.5625 6.2300 0.0000 15.7858 −0.3695 0.0000 17.0597 6.21930.0000 16.2176 −0.4016 0.0000 17.5576 6.1972 0.0000 16.6481 −0.43740.0000 18.0561 6.1633 0.0000 17.0786 −0.4777 0.0000 18.5546 6.11730.0000 17.5079 −0.5212 0.0000 19.0531 6.0594 0.0000 17.9359 −0.56900.0000 19.5497 5.9895 0.0000 18.3639 −0.6212 0.0000 20.0425 5.90710.0000 18.7913 −0.6773 0.0000 20.5322 5.8133 0.0000 19.2174 −0.73770.0000 21.0175 5.7069 0.0000 19.6422 −0.8019 0.0000 21.4990 5.58920.0000 20.0671 −0.8711 0.0000 21.9774 5.4589 0.0000 20.4907 −0.94480.0000 22.4513 5.3167 0.0000 20.9137 −1.0228 0.0000 22.9221 5.16190.0000 21.3354 −1.1059 0.0000 23.3892 4.9957 0.0000 21.7565 −1.19340.0000 23.8530 4.8169 0.0000 22.1769 −1.2859 0.0000 24.3131 4.62620.0000 22.5961 −1.3835 0.0000 24.7701 4.4229 0.0000 23.0140 −1.48610.0000 25.2233 4.2077 0.0000 23.4313 −1.5937 0.0000 25.6708 3.98170.0000 23.8474 −1.7064 0.0000 26.1114 3.7457 0.0000 24.2628 −1.82470.0000 26.5451 3.4996 0.0000 24.6770 −1.9487 0.0000 26.9712 3.24460.0000 25.0905 −2.0783 0.0000 27.3904 2.9803 0.0000 25.5021 −2.21300.0000 27.8026 2.7071 0.0000 25.9131 −2.3540 0.0000 28.2080 2.42580.0000 26.3229 −2.5013 0.0000 28.6070 2.1356 0.0000 26.7320 −2.65490.0000 28.9998 1.8379 0.0000 27.1392 −2.8141 0.0000 29.3863 1.53200.0000 27.5458 −2.9803 0.0000 29.7671 1.2179 0.0000 27.9499 −3.15280.0000 30.1416 0.8969 0.0000 28.3502 −3.3302 0.0000 30.5110 0.56840.0000 28.7461 −3.5140 0.0000 30.8748 0.2316 0.0000 29.1376 −3.70290.0000 31.2330 −0.1114 0.0000 29.5254 −3.8974 0.0000 31.5861 −0.46200.0000 29.9087 −4.0969 0.0000 31.9341 −0.8189 0.0000 30.2882 −4.30270.0000 32.2759 −1.1820 0.0000 30.6627 −4.5136 0.0000 32.6127 −1.55030.0000 31.0334 −4.7307 0.0000 32.9437 −1.9241 0.0000 31.3991 −4.95290.0000 33.2691 −2.3024 0.0000 31.7610 −5.1814 0.0000 33.5882 −2.68570.0000 32.1179 −5.4155 0.0000 33.9023 −3.0734 0.0000 32.4710 −5.65530.0000 34.2107 −3.4656 0.0000 32.8197 −5.9008 0.0000 34.5135 −3.86150.0000 33.1634 −6.1519 0.0000 34.8112 −4.2624 0.0000 33.5026 −6.40940.0000 35.1039 −4.6659 0.0000 33.8375 −6.6731 0.0000 35.3922 −5.07370.0000 34.1667 −6.9431 0.0000 35.6767 −5.4835 0.0000 34.4908 −7.22130.0000 35.9580 −5.8964 0.0000 34.8087 −7.5058 0.0000 36.2356 −6.31180.0000 35.1215 −7.7985 0.0000 36.5113 −6.7285 0.0000 35.4280 −8.09810.0000 36.7838 −7.1470 0.0000 35.7289 −8.4059 0.0000 37.0538 −7.56750.0000 36.0254 −8.7193 0.0000 37.3188 −7.9905 0.0000 36.3174 −9.03840.0000 37.5788 −8.4172 0.0000 36.6063 −9.3620 0.0000 37.8318 −8.84770.0000 36.8914 −9.6905 0.0000 38.0791 −9.2820 0.0000 37.1728 −10.02280.0000 38.3221 −9.7188 0.0000 37.4510 −10.3608 0.0000 38.5569 −10.16010.0000 37.7254 −10.7026 0.0000 38.6299 −10.3514 0.0000 37.8758 −10.84990.0000 38.6525 −10.5541 0.0000 38.0590 −10.9525 0.0000 38.5965 −10.74790.0000 38.2655 −10.9733 0.0000 38.4599 −10.8971 0.0000 38.4599 −10.89710.0000 1.1499 0.6640 10.0002 1.1499 0.6640 10.0002 1.1588 1.1380 10.00021.3721 0.3135 10.0002 1.3967 1.5559 10.0002 1.7353 0.1070 10.0002 1.71451.9191 10.0002 2.1369 −0.0101 10.0002 2.0702 2.2451 10.0002 2.5485−0.0799 10.0002 2.4497 2.5435 10.0002 2.9627 −0.1152 10.0002 2.84622.8192 10.0002 3.3768 −0.1259 10.0002 3.2547 3.0766 10.0002 3.7916−0.1164 10.0002 3.6727 3.3177 10.0002 4.2070 −0.0887 10.0002 4.09883.5443 10.0002 4.6224 −0.0478 10.0002 4.5318 3.7576 10.0002 5.03720.0025 10.0002 4.9705 3.9584 10.0002 5.4520 0.0560 10.0002 5.4130 4.149810.0002 5.8668 0.1095 10.0002 5.8586 4.3335 10.0002 6.2816 0.158610.0002 6.3055 4.5098 10.0002 6.6970 0.2033 10.0002 6.7549 4.679710.0002 7.1124 0.2448 10.0002 7.2062 4.8440 10.0002 7.5278 0.283910.0002 7.6594 5.0026 10.0002 7.9439 0.3204 10.0002 8.1145 5.154310.0002 8.3599 0.3537 10.0002 8.5714 5.2984 10.0002 8.7760 0.383910.0002 9.0315 5.4363 10.0002 9.1920 0.4104 10.0002 9.4935 5.565910.0002 9.6087 0.4337 10.0002 9.9574 5.6887 10.0002 10.0254 0.453810.0002 10.4244 5.8032 10.0002 10.4420 0.4702 10.0002 10.8933 5.909610.0002 10.8593 0.4834 10.0002 11.3654 6.0078 10.0002 11.2773 0.492810.0002 11.8393 6.0972 10.0002 11.6946 0.4985 10.0002 12.3146 6.177110.0002 12.1125 0.5004 10.0002 12.7910 6.2476 10.0002 12.5304 0.498510.0002 13.2688 6.3087 10.0002 12.9490 0.4928 10.0002 13.7459 6.359010.0002 13.3669 0.4828 10.0002 14.2230 6.3993 10.0002 13.7849 0.468910.0002 14.7007 6.4295 10.0002 14.2028 0.4513 10.0002 15.1784 6.447810.0002 14.6195 0.4286 10.0002 15.6568 6.4553 10.0002 15.0362 0.402210.0002 16.1358 6.4515 10.0002 15.4522 0.3720 10.0002 16.6160 6.435810.0002 15.8670 0.3367 10.0002 17.0969 6.4081 10.0002 16.2811 0.297110.0002 17.5771 6.3678 10.0002 16.6940 0.2530 10.0002 18.0574 6.316210.0002 17.1057 0.2046 10.0002 18.5351 6.2520 10.0002 17.5167 0.151710.0002 19.0109 6.1758 10.0002 17.9264 0.0938 10.0002 19.4836 6.087710.0002 18.3356 0.0315 10.0002 19.9519 5.9877 10.0002 18.7434 −0.035910.0002 20.4171 5.8756 10.0002 19.1507 −0.1076 10.0002 20.8784 5.751610.0002 19.5566 −0.1850 10.0002 21.3360 5.6157 10.0002 19.9620 −0.266910.0002 21.7898 5.4678 10.0002 20.3661 −0.3537 10.0002 22.2398 5.308510.0002 20.7695 −0.4456 10.0002 22.6867 5.1373 10.0002 21.1711 −0.543210.0002 23.1305 4.9541 10.0002 21.5720 −0.6458 10.0002 23.5711 4.759710.0002 21.9717 −0.7534 10.0002 24.0079 4.5532 10.0002 22.3708 −0.867310.0002 24.4397 4.3373 10.0002 22.7686 −0.9863 10.0002 24.8651 4.110710.0002 23.1657 −1.1109 10.0002 25.2837 3.8760 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100.000015.2653 8.4518 100.0000 14.2519 5.8309 100.0000 15.5372 8.3184 100.000014.4961 5.6987 100.0000 15.8059 8.1780 100.0000 14.7384 5.5628 100.000016.0709 8.0301 100.0000 14.9783 5.4218 100.0000 16.3321 7.8759 100.000015.2155 5.2758 100.0000 16.5896 7.7160 100.0000 15.4509 5.1266 100.000016.8438 7.5499 100.0000 15.6838 4.9724 100.0000 17.0944 7.3787 100.000015.9155 4.8150 100.0000 17.3417 7.2024 100.0000 16.1446 4.6533 100.000017.5853 7.0218 100.0000 16.3718 4.4884 100.0000 17.8251 6.8367 100.000016.5977 4.3197 100.0000 18.0618 6.6485 100.0000 16.8212 4.1485 100.000018.2953 6.4572 100.0000 17.0421 3.9741 100.0000 18.5257 6.2621 100.000017.2605 3.7973 100.0000 18.7529 6.0638 100.0000 17.4770 3.6185 100.000018.9776 5.8630 100.0000 17.6910 3.4379 100.0000 19.1991 5.6597 100.000017.9032 3.2541 100.0000 19.4188 5.4533 100.0000 18.1134 3.0690 100.000019.6353 5.2449 100.0000 18.3217 2.8821 100.0000 19.8506 5.0335 100.000018.5282 2.6926 100.0000 20.0633 4.8201 100.0000 18.7334 2.5019 100.000020.2735 4.6048 100.0000 18.9367 2.3100 100.0000 20.4819 4.3870 100.000019.1387 2.1161 100.0000 20.6890 4.1674 100.0000 19.3389 1.9204 100.000020.8935 3.9458 100.0000 19.5378 1.7233 100.0000 21.0968 3.7224 100.000019.7354 1.5251 100.0000 21.2982 3.4970 100.0000 19.9318 1.3256 100.000021.4978 3.2698 100.0000 20.1269 1.1248 100.0000 21.6954 3.0413 100.000020.3208 0.9227 100.0000 21.8918 2.8110 100.0000 20.5140 0.7194 100.000022.0863 2.5794 100.0000 20.7053 0.5149 100.0000 22.2789 2.3465 100.000020.8960 0.3097 100.0000 22.4702 2.1117 100.0000 21.0855 0.1032 100.000022.6597 1.8763 100.0000 21.2743 −0.1045 100.0000 22.8479 1.6396 100.000021.4619 −0.3135 100.0000 23.0342 1.4011 100.0000 21.6488 −0.5224100.0000 23.2186 1.1619 100.0000 21.8351 −0.7326 100.0000 23.4018 0.9215100.0000 22.0202 −0.9441 100.0000 23.5837 0.6798 100.0000 22.2040−1.1562 100.0000 23.7637 0.4368 100.0000 22.3878 −1.3684 100.000023.9424 0.1932 100.0000 22.5703 −1.5817 100.0000 24.1199 −0.0516100.0000 22.7516 −1.7957 100.0000 24.2955 −0.2977 100.0000 22.9328−2.0104 100.0000 24.4705 −0.5444 100.0000 23.1128 −2.2256 100.000024.6436 −0.7924 100.0000 23.2922 −2.4415 100.0000 24.8154 −1.0417100.0000 23.4710 −2.6580 100.0000 24.9854 −1.2916 100.0000 23.6485−2.8752 100.0000 25.1547 −1.5427 100.0000 23.8260 −3.0930 100.000025.3221 −1.7945 100.0000 24.0028 −3.3107 100.0000 25.4883 −2.0469100.0000 24.1785 −3.5298 100.0000 25.6532 −2.3012 100.0000 24.3541−3.7488 100.0000 25.8162 −2.5554 100.0000 24.5290 −3.9685 100.000025.9780 −2.8110 100.0000 24.7034 −4.1881 100.0000 26.1385 −3.0672100.0000 24.8771 −4.4091 100.0000 26.2977 −3.3246 100.0000 25.0502−4.6300 100.0000 26.4557 −3.5826 100.0000 25.2227 −4.8509 100.000026.6124 −3.8413 100.0000 25.3945 −5.0731 100.0000 26.7679 −4.1007100.0000 25.5657 −5.2959 100.0000 26.9233 −4.3606 100.0000 25.7356−5.5194 100.0000 27.0769 −4.6206 100.0000 25.9049 −5.7434 100.000027.2305 −4.8811 100.0000 26.0730 −5.9681 100.0000 27.3828 −5.1423100.0000 26.2398 −6.1935 100.0000 27.5351 −5.4042 100.0000 26.4060−6.4201 100.0000 27.6862 −5.6660 100.0000 26.5709 −6.6473 100.000027.8366 −5.9285 100.0000 26.7345 −6.8751 100.0000 27.9864 −6.1910100.0000 26.8969 −7.1042 100.0000 28.1356 −6.4547 100.0000 27.0593−7.3333 100.0000 28.2835 −6.7184 100.0000 27.2204 −7.5631 100.000028.4295 −6.9834 100.0000 27.3822 −7.7928 100.0000 28.5730 −7.2490100.0000 27.5446 −8.0219 100.0000 28.7153 −7.5165 100.0000 27.7070−8.2504 100.0000 28.8544 −7.7853 100.0000 27.8700 −8.4789 100.000028.9916 −8.0547 100.0000 28.0324 −8.7080 100.0000 29.1276 −8.3253100.0000 28.1941 −8.9371 100.0000 29.2623 −8.5960 100.0000 28.3584−9.1650 100.0000 29.3938 −8.8685 100.0000 28.5233 −9.3922 100.000029.5203 −9.1436 100.0000 28.6857 −9.6213 100.0000 29.5826 −9.3343100.0000 28.8254 −9.7723 100.0000 29.5952 −9.5332 100.0000 28.9979−9.8837 100.0000 29.5329 −9.7201 100.0000 29.1974 −9.9190 100.000029.3913 −9.8592 100.0000 29.3913 −9.8592 100.0000

It will also be appreciated that the airfoil 52 disclosed in the aboveTable I may be scaled up or down geometrically for use in other similarturbine designs. Consequently, the coordinate values set forth in TableI may be scaled upwardly or downwardly such that the airfoil profileshape remains unchanged. A scaled version of the coordinates in Table Iwould be represented by X, Y and Z coordinate values of Table I, withthe X, Y and Z non-dimensional coordinate values converted to units ofdistance (e.g., inches), multiplied or divided by a constant number.

An important term in this disclosure is “profile”. The profile is therange of the variation between measured points on an airfoil surface andthe ideal position listed in Table I. The actual profile on amanufactured turbine rotor blade will be different than those in TableI, and the design is robust to this variation meaning that mechanicaland aerodynamic function are not impaired. As noted above, a + or −5%profile tolerance is used herein. The X, Y and Z values are allnon-dimensionalized relative to the airfoil height.

The disclosed airfoil shape optimizes and is specific to the machineconditions and specifications. It provides a unique profile toachieve 1) interaction between other stages in the turbine 10; 2)aerodynamic efficiency, and 3) normalized aerodynamic and mechanicalblade loadings. The disclosed loci of points defined in Table I allowthe gas turbine 12 or any other suitable turbine to run in an efficient,safe and smooth manner. As also noted, the disclosed airfoil 52 may beadapted to any scale, as long as 1) interaction between other stages inthe pressure turbine 10; 2) aerodynamic efficiency; and 3) normalizedaerodynamic and mechanical blade loadings are maintained in the scaledturbine.

The airfoil 52 described herein thus improves overall gas turbine 12efficiency. Specifically, the airfoil 52 provides a desired turbineefficiency lapse rate (ISO, hot, cold, part load, etc.). The airfoil 52also meets all aeromechanical and stress requirements. The turbine rotorblade 50 described herein has very specific aerodynamic designrequirements, such as an upstream bucket radial back pressure (i.e.,work splits) and radial velocity triangles for the downstream turbinerotors 150, 250, 350 and 450. Significant cross-functional design effortwas required to meet these design goals. The airfoil 52 of the turbinerotor blade 50 thus is of a specific shape to meet aerodynamic,mechanical, and heat transfer requirements in an efficient andcost-effective manner.

This written description uses examples to disclose the invention,including the best mode, and also to enable any person skilled in theart to practice the invention, including making and using any devices orsystems and performing any incorporated methods. The patentable scope ofthe invention is defined by the claims and may include other examplesthat occur to those skilled in the art. Such other examples are intendedto be within the scope of the claims, if they have structural elementsthat do not differ from the literal language of the claims or if theyinclude equivalent structural elements with insubstantial differencesfrom the literal languages of the claims.

What is claimed is:
 1. A turbine rotor blade comprising an airfoilhaving an airfoil shape, the airfoil shape having a nominal profilesubstantially in accordance with Cartesian coordinate values of X, Y andZ set forth in Table I, wherein the Cartesian coordinate values of X, Yand Z are non-dimensional values from 0% to 100% convertible todimensional distances expressed in a unit of distance by multiplying theCartesian coordinate values of X, Y and Z by a height of the airfoil inthe unit of distance; and wherein X and Y values, when connected bysmooth continuing arcs, define airfoil profile sections at each Z value,the airfoil profile sections at Z values being joined smoothly with oneanother to form a complete airfoil shape.
 2. The turbine rotor blade ofclaim 1, wherein the turbine rotor blade forms part of a stage of aturbine.
 3. The turbine rotor blade of claim 1, wherein the turbinerotor blade is a third stage turbine rotor blade.
 4. The turbine rotorblade of claim 1, wherein the airfoil shape lies in an envelope withinat least one of +/−5% and/or +/−5% of a chord length in a directionnormal to any airfoil surface location.
 5. The turbine rotor blade ofclaim 1, wherein the height of the airfoil is about 10 inches to about20 inches.
 6. The turbine rotor blade of claim 1, wherein the X, Y and Zvalues are scalable as a function of the same constant or number toprovide a scaled-up or scaled-down airfoil.
 7. A turbine rotor bladecomprising an airfoil having an uncoated nominal suction-side profilesubstantially in accordance with suction-side Cartesian coordinatevalues of X, Y and Z set forth in Table I, wherein the Cartesiancoordinate values of X, Y and Z are non-dimensional values from 0% to100% convertible to dimensional distances expressed in a unit ofdistance by multiplying the Cartesian coordinate values of X, Y and Z bya height of the airfoil in the unit of distance; and wherein X and Yvalues, when connected by smooth continuing arcs, define airfoil profilesections at each Z value, the airfoil profile sections at the Z valuesbeing joined smoothly with one another to form a complete suction-sideairfoil shape.
 8. The turbine rotor blade of claim 7, wherein theturbine rotor blade forms part of a stage of a turbine.
 9. The turbinerotor blade of claim 7, wherein the turbine rotor blade is a third stageturbine rotor blade.
 10. The turbine rotor blade of claim 7, wherein thesuction-side shape lies in an envelope within at least one of +/−5%and/or +/−5% of a chord length in a direction normal to any airfoilsurface location.
 11. The turbine rotor blade of claim 7, wherein theheight of the airfoil is about 10 inches to about 20 inches.
 12. Theturbine rotor blade of claim 7, wherein the X, Y, and Z values arescalable as a function of the same constant or number to provide ascaled-up or scaled-down airfoil with the complete airfoil suction-sideshape.
 13. A turbine comprising a plurality of turbine rotor blades,each of the turbine rotor blades comprising an airfoil having an airfoilshape, the airfoil having a nominal profile substantially in accordancewith Cartesian coordinate values of X, Y and Z set forth in Table I,wherein the Cartesian coordinate values of X, Y and Z arenon-dimensional values from 0% to 100% convertible to dimensionaldistances expressed in a unit of distance by multiplying the Cartesiancoordinate values of X, Y and Z by a height of the airfoil in the unitof distance; and wherein X and Y values, when connected by smoothcontinuing arcs, define airfoil profile sections at each Z value, theairfoil profile sections at Z values being joined smoothly with oneanother to form a complete airfoil shape.
 14. The turbine of claim 13,wherein the plurality of turbine rotor blades forms part of a stage of aturbine.
 15. The turbine of claim 13, wherein the plurality of turbinerotor blades comprises a plurality of third stage turbine rotor blades.16. The turbine of claim 13, wherein the airfoil shape lies in anenvelope within at least one of +/−5% and/or +/−5% of a chord length ina direction normal to any airfoil surface location.
 17. The turbine ofclaim 13, wherein the height of the airfoil is about 10 inches to about20 inches.
 18. The turbine of claim 12, wherein the X, Y and Z valuesare scalable as a function of the same constant or number to provide ascaled-up or scaled-down airfoil.
 19. The turbine of claim 12, wherein Xrepresents a distance parallel to a turbine axis of rotation.